Operational amplifiers (op amps) are fundamental elements in various analog circuit designs. An example of an op amp 1200 is shown in FIG. 12. Op amp 1200 can include a positive input (+), a negative input (−), and can generate an output voltage Vout on an output 1291. Ideally, an op amp 1200 operates according to the response Vout=Gain*(IN(+)−IN(−)), where Gain is the open loop gain of the op amp, IN(+) is the voltage at the (+) input and IN(−) is the voltage at the (−) input. Accordingly, in an ideal op amp, when a common voltage is applied to both the (+) input and (−) input, an output voltage would be zero.
In reality, when a common voltage is applied to both inputs of an op amp, Vout will not be zero, due to uncontrollable variations in the op amp components and/or materials. For example, an op amp typically has a differential input stage with input transistors designed to match one another. These matching input transistors are designed to have the same size and to be fabricated with the same process steps. However, mismatch between input transistors can occur. As but a few examples, there may be mismatch due to essentially random effects, such as edge effects during photolithography, material imperfections, and variations in carrier mobility. Device mismatch can cause differences between the input transistors, including differences in transistor threshold voltage (Vt), conductance parameter K, and body effect parameter γ.
A differential voltage applied between the (+) and (−) inputs of an op amp which results in a zero output voltage (i.e., a voltage that cancels mismatching) is called the input offset voltage (Voffset) of the op amp.
Conventional approaches to addressing input offset voltage include “auto-zeroing” type op amps, adjusting biasing currents in an input stage, or digital adjustment of input device size. Auto-zeroing op amps can result in larger circuit size and operation complexity. Adjusting biasing currents can also increase circuit complexity, particularly when very fine changes in current are needed over a range of operating temperatures and/or voltages. Digitally adjusting device size may result in better size matching, but random variations in materials can still give rise to an input offset voltage.